The uncertainties associated with the coupling between successive Monte Carlo (MC) steps and the integration of the (non-linear) differential equations were carefully studied by Brandan et al. [77]. They found that an integration step equal to one fifth of the shortest nuclide half-life was sufficient to reach convergence of the solution to the differential equations. They anticipate two types of error: statistical errors in the average cross­section determination after one MC step, and systematic errors due to the evolution of these cross-sections during the time of a single MC calculation.

The CPU time devoted to each MC step was fixed, thus fixing the total number of neutrons being followed and the statistical errors at all cycles, independent of the system multiplication. For instance, a CPU equal to 15 min (in a DEC Alpha 500/500 workstation) permits one to follow some 20 000 neutrons, which correspond to 400 source neutrons for a typical ks = 0.98. This way, the statistical errors in the calculated cross-sections were typically less than 10% in each cell. However, the total error after a series of MC steps may depend dramatically on the particular nucleus being studied. Tests were performed simulating the evolution of a 233U reactor over 5 years. In a first case, the differential equations were solved every 3 months of operation, i. e. the complete evolution included a total of 20 MC steps. These results were compared with a second case, with only one MC step for the 5-year solution.

Figure 5.8 illustrates the resulting time evolution of the number of 239Pu and 244Cm nuclei during the last year at the end of the evolution, for the two cases. The data points and thick curve show the results from the 20-step calculation. The thin solid curves show independent one-step results and the dashed curve represents their average. The dispersion of the one-step results reflects statistical fluctuations in the initial average cross-sections. These fluctuations, indicated in figure 5.8 by the (F) arrows, reach ~1% of the average for the production of 239Pu and ~10% for the production of 244Cm. Arrows (S) in figure 5.8 show the (systematic) discrepancies between the two procedures. The systematic error that could be made when treating the 5 year evolution with only one intermediate integration is of the order of 1% for 239Pu and of 20% for 244Cm. The difference

Time (y)

between these nuclei is due to the time evolution of their mean cross-sections, caused by the neutron spectral evolution during the operation. As figure 5.8 has shown, this variation cannot be properly taken into account by one-step calculations. All the results reported by Brandan et al. [77] have been obtained with 15 minute CPU Monte Carlo simulations per step and

20 MC steps per 5 year calculation; test calculations have shown that the systematic errors associated with this choice are negligible. Examples of particular cases where this detailed approach is absolutely required have been given by David et al. [79].

Some fission products like 135Xe and [47]Sm have very large absorption cross­sections for thermal neutrons. They are not produced directly by fission but by beta decay of precursor fission fragments. The decay chains by which they are produced as

135Xe has an absorption cross-section of 2.7 x 106 barns for thermal (0.025 eV) neutrons, while that of 149Sm is 40 800 barns. Because of the dominant effect of 135Xe we give the derivation of the xenon effect. The evolution equations read

where we have neglected captures by iodine. yI ‘ 0.06 is the yield of mass 135 in fission. At equilibrium

yI^f’

nI

yA’

nXe =t—— :———

AXe + °Xe’

for a flux of 4 x 1013 n/cm2/s, o-Xe’ = 10—4 AXe = 2 x 10—5. Thus

It follows that

у = -0.03.

After a reactor shut-down, the evolution of xenon is given by

which yields

Figure 8.3 shows the evolution of the xenon-induced reactivity decrease after shut-down of a thermal reactor at two flux levels: 4 x 1013 and 2 x 1014n/cm2/s.

It is remarkable that, as apparent from equation (8.19), the initial xenon concentration is independent of the neutron flux, at least for fluxes that are not too small. In critical reactors the reactivity decrease prevents restarting of the reactor if a large enough positive reactivity reserve is not available. Hybrid systems can be restarted at any time, although the gain will be smaller if the xenon concentration is high. However, if the reactor is

stopped long enough, the xenon concentration vanishes and thus the reactivity is larger by 0.0035 than the reactivity during operation. This is true for any thermal reactor, and has to be added to the protactinium — related reactivity increase, in the case of thorium reactors. For fast reactors the xenon effect is negligible.

To describe the breeding performances of such a system, we can use the conversion ratio C, which is defined by the ratio between the 233 U production rate by Pa decay, and the U feeding flow. If one chooses a reprocessing time of 10 days, which seems to be a minimal value, this type of molten salt reactor leads to a conversion ratio C at equilibrium of 1.05. The 233Pa inventory is around 20 kg in the core.

It appears clear that the deployment ability of the asymptotic Th/U MSR is better than that of fast neutron thorium reactors. The doubling time is around 25 years. This favourable behaviour is essentially due to the reduced fissile inventory. One has then to study the possibility of reaching the asymptotic Th/U cycle, starting Th/Pu reactors with the plutonium coming from the PWR spent fuel.

Different reprocessing methods can be considered, depending on the desired scenarios. Complex and fast reprocessing, where a lot of nuclei are extracted during a short time, will lead to a very good neutron balance and large breeding rates. This makes a fast development of such reactors possible. On the contrary, if fast development is not the priority, the

reprocessing principle can be largely simplified by increasing the reprocessing time or by reprocessing only a few nuclei.

In the same vein, the reprocessing can be simplified by the use of an accelerator driven molten salt reactor. For example, the performance, in term of breeding rates, of a critical reactor using an online 233Pa extraction is similar to that of an accelerator driven system, running at k = 0.98, without protactinium extraction.

In theory, the future disposal site should hold the vitrified reprocessed irradiated fuel, the UOx fuel that has not been reprocessed and, possibly, MOx irradiated fuel. Globally, reprocessing decreases the long-term radio­toxicity of the waste by significantly decreasing the amounts of plutonium and iodine it contains. Here, we will consider only the non-reprocessed fuels, i. e. the maximum potential radioactivity losses.

In table I.2, the composition of 20 000 metric tons of irradiated fuel (IF) at the reactor discharge time is given. This amount corresponds to approxi­mately 10 years’ operation of the reactors that are running today in France. It shows that the largest activities at discharge are those of 90Sr, 137Cs and 241Am which have half-lives shorter than 50 years. These activities will be sharply reduced 100 years after discharge. This is why an interim storage with at least such duration is, almost always, thought necessary before deep underground storage. Such interim storage would also reduce consider­ably the activity of 244Cm, which is known to be a strong neutron emitter.

When compared with critical reactors, ADSRs have two specific charac­teristics.

1. If well designed, they prevent any possible criticality accidents. This has led their most vocal advocates [45] to propose that they should replace critical reactors altogether. In a less radical but also more common approach it has been proposed [38, 46] to take advantage of this sub­criticality in order to use certain types of fuel with poor neutronic properties: in particular, because of their very small delayed neutron fractions, homogeneous incineration of minor actinides appears to be feasible only with subcritical reactors.

2. Subcriticality provides additional neutrons which can be used for increased breeding of U or 9Pu. It is even possible to breed them in the absence of any fissile element. Another possible use of the additional neutrons is to transmute long-lived fission products.

Let us elaborate on these points.

The most documented type of liquid metal reactor is the sodium cooled reactor. Here the coolant is liquid sodium at a temperature of 500 °C, while the boiling temperature of sodium at atmospheric pressure is 883 °C. The pressure within the vessel is slightly above 1 atm of argon gas, in order to prevent air intrusion. The most modern sodium cooled reactors like Phenix and Superphenix [63] are of the swimming pool type. These characteristics practically prevent loss of coolant accidents. The negative temperature reactivity coefficients have been shown to lead to a break-off of the chain reaction and to a moderate temperature increase within minutes, for the small EBR2 (20 MWe) reactor. For Phenix (250 MWe) natural convection was demonstrated to evacuate the residual heat. In general it appears that sodium cooled reactors are much safer than water cooled reactors with respect to core melting. The risk for an individual living in the vicinity of the reactor to die from a cancer induced by accidental radioactivity release is estimated to be around 10~10 for these reactors.

The main safety concern with sodium cooled reactors is, precisely, with the use of sodium which burns spontaneously when in contact with air and dissociates water, with the consequent risk of a hydrogen explosion. The risk associated with violent sodium-water reactions explains the choice made by the former USSR to use a molten bismuth-lead eutectic as coolant for their most modern nuclear submarine reactors. It also prompted the recent proposal of the CERN group [76]. In addition lead has a boiling temperature of 1749 °C, which makes coolant boiling completely impossible, due to radiation cooling. A swimming pool type lead cooled reactor would have a very high safety level.

5.5.1 Introduction

The aim of this part is to present some reactor simulation examples; it cannot replace the MCNP reference manual.

When MCNP is running, two special files are needed; one is, of course, the problem description (geometry, materials, neutron source, etc.). The other one, named xsdir, is a special file that contains some nuclear data and the path of the ENDF library files for each material. This file can be placed in a default directory, but MCNP first looks in the ‘current’ directory if such a file exists.

5.5.2 Units

The specific units used in MCNP are summarized in table 5.1.

Another very important characteristic of spallation reactions is the nature of the heavy residues. This reflects the light particle emission rates and deter­mines the radiotoxicity of the wastes of the spallation reaction. In particular, for heavy target nuclei like lead, the amount of 194Hg created is a key quantity since 194Hg has a long half-life of 520 years and decays to 194Au which has a short lifetime of 38 hours and a large decay energy of

2.5 MeV. Thus the decay of 194Hg is both long lived and energetic. Up until recently determination of residue mass and charge distributions used standard radiochemical techniques, mostly gamma ray counting of the reac­tion products. The most extensive study has been that by Michel et al. [111]. This technique is based on the observation of gamma decays following beta decays, and thus misses stable residues as well as very long-lived ones whose activity is too weak to be visible. Recently, the very beautiful inverse kinematic technique promoted in GSI, for fission studies and neutron-rich nuclei synthesis, has been used to tackle the residue question. This technique, essentially, allows determination of all yields of heavy residues and fission fragments. These yields are measured immediately after the reaction and thus cannot be compared directly with those obtained from radiochemical measurements. However, for the so-called shielded isotopes which are directly produced by the reaction mechanism, a direct comparison between the two techniques can be done, and is found to be satisfactory [112]. Figure 6.5 shows a comparison between the experimental data and a few cal­culations for the reaction p + Au (0.8 GeV/A). All calculations reported use the Dresner evaporation code. The figure shows a significant improvement when using modern INC calculations for the region of spallation products. However, fission appears to be under-evaluated. Figure 6.6 shows that an

even better agreement is obtained if the Dresner evaporation code is replaced by a modern evaporation code elaborated at GSI [113].

Thorium has a distribution coefficient in TBP smaller by an order of magni­tude than uranium. This makes thorium extraction by TBP more difficult than that of uranium. In particular, much larger fluxes of TBP are required for the same extracted quantity. Such an extraction, called the Thorex process, has been achieved at a pre-industrial stage in two instances [138]:

• At Hanford more than 200 metric tons of low-burn-up aluminium-clad thorium fuel were processed [142].

• In the frame of the THTR (thorium high-temperature reactor), laboratory extraction of thorium and uranium was carried out at Jiilich on highly irradiated fuels [143].

Aside from a low distribution coefficient, thorium extraction is made difficult by the existence of an additional organic phase which appears for a rather modest thorium nitrate concentration in the aqueous phase. This concentration decreases as a function of the concentration of nitric acid. Furthermore it was found that at moderate nitric acid concentrations, needed for good separation of thorium from fission products (around 1.5mol/l), fission products, if present in large quantities, might precipitate. This has led [143, 144] to a rather complicated extraction process where an initial pre-decontamination of thorium and uranium with low thorium (1.15mol/l) and medium nitric acid (1mol/l) concentrations, was followed by an extraction stage with lower nitric acid concentration (0.15mol/l) and, finally, separation and purification of thorium and uranium. The Purex process is unable to separate thorium from protactinium with good efficiency. An improved separation can be obtained by adding phosphoric acid H3PO4 which complexes readily with protactinium.

An interesting aspect of the Jiilich experiment is that it involved the treatment of fuel particles embedded in graphite and silicon carbide spheres. The graphite was burned in oxygen to CO2. Because of the presence of 14C this has to be sequestered in the form of CaCO3, for example.

Thus the treatment of thorium fuels by the Purex process has been demonstrated but leads to much larger radioactive effluents than does the Purex process for uranium and plutonium extraction.

Molten salt fuels give the possibility of quasi-online treatment and purification, allowing a very good control of the reactivity, as well as neutron economy optimization by preventing neutron losses by capture by fission products. Some of the earliest hybrid reactor proposals were based on molten salt fuels [1]. As an example we describe the proposal made by Bowman [2].